Dewetting of thin polymer films

We study the dewetting of thin polymer films deposited on slippery substrate. Recent experiments on these systems have revealed many unexpected features. We develop here a model that takes into account the rheological properties of polymer melts, focussing on two dewetting geometries (the receding of a straight edge, and the opening of a hole). We show that the friction law associated with the slippage between the film and the substrate has a direct influence on the dewetting dynamic. In addition, we demonstrate that residual stresses, which can be stored in the films due to their viscoelasticity, are a source of destabilization for polymer films, and accelerate the dewetting process.     

Viscoelastic dewetting of a polymer film on a liquid substrate

The Dewetting of thin polymer films (60–300 nm) on a non-wettable liquid substrate has been studied in the vicinity of their glass transition temperature. In our experiment, we observe a global contraction of the film while its thickness remains uniform. We show that, in this case, the strain corresponds to simple extension, and we verify that it is linear with the stress applied by the surface tension. This allows direct measurement of the stress/strain response as a function of time, and thus permits the measurement of an effective compliance of the thin films. It is, however, difficult to obtain a complete viscoelastic characterization, as the short time response is highly dependant on the physical age of the sample. Experimental results underline the effects of residual stress and friction when dewetting is analyzed on rigid substrates.     

Morphologies of diblock copolymer thin films before and after crystallization

Spin-coated thin films of about 100nm of low-molecular-weight hydrogenated poly(butadiene-b- ethyleneoxide) (PB_h-PEO) diblock copolymers have been crystallized at various constant temperatures. Crystallization has been observed in real time by light microscopy. Detailed structural information was obtained by atomic force microscopy, mainly enabled by the large viscoelastic contrast between amorphous and crystalline regions. The behavior in thin films is compared to the bulk properties of the polymer. Crystallization started from an annealed microphase separated melt where optical microscopy indicated a lamellar orientation parallel to the substrate. A small difference in the length of the crystallizable block produced significantly different crystallization behavior, both in the bulk and in thin films. For thin films of the shortest diblock copolymer (45% PEO content) and for an undercooling larger than about 10 degrees, crystallization created vertically oriented lamellae. These vertical lamellae could be preferentially aligned over several micrometers when crystallization occurred close to a three-phase contact line. Annealing at temperatures closer to the melting point or keeping the sample at room temperature for several months allowed the formation of a lamellar structure parallel to the substrate. A tentative interpretation based on kinetically caused chain folding and relaxation within the crystalline state, with implications on general aspects of polymer crystallization, is presented. Received 19 March 1999 and Received in final form 14 December 1999     

Effect of physical ageing in thin glassy polymer films

We have studied the effect of physical ageing in thin supported glassy polystyrene films by using ellipsometry to detect overshooting in the expansivity-temperature curve upon heating of aged samples. Films with thickness 10-200 nm have been aged at 70^° C and 80^° C (below the bulk glass transition temperature). We observe clear relaxation peaks in the expansivity-temperature curve for films thicker than 18 nm but not for the 10 nm film. The intensity of the relaxation peak is inversely proportional to the film thickness, while the temperatures characteristic to the relaxation peak are almost independent of the film thickness. These observations are successfully interpreted by the idea that the surface layer of the order of 10 nm has liquid-like thermal properties. Received 28 October 2002 / Published online: 1 April 2003 RID="a" ID="a"Present address: Yokohama Research Center, Mitsubishi Chemical Corporation, 1000 Kamoshida-chou, Aoba-ku, Yokohama 227-8502, Japan; e-mail: kawana@rc.m-kagaku.co.jp     

Molecular dynamics of hyperbranched polyesters in the confinement of thin films

Broadband Dielectric Spectroscopy is employed to investigate the molecular dynamics in thin films of hyperbranched polyesters (type AB₁B₂, with -OH and -OCOCH₃ as terminal groups). Three relaxation processes are detected: alpha, beta and gamma. While the latter two are not influenced by the confinement, a pronounced effect is observed on the alpha relaxation: with decreasing film thickness the slower relaxation modes of the dynamic glass transition are gradually suppressed, resulting in an increase of the average relaxation rate and in a linear decrease of the dielectric strength. This is attributed to an immobilization in confinement of the polymeric segments located at the periphery of the hyperbranched macromolecular structures.     

Some relevant parameters affecting the glass transition of supported ultra-thin polymer films

We have measured, the thickness dependence of the glass transition temperature T(g)( h), using ellipsometry at variable temperature, for poly(methyl-methacrylate) (PMMA) of various tacticity in confined geometry. We report that several factors significantly affect T(g)( h): i) polymer microstructure (stereoregularity of PMMA) related to local dynamics; ii) interfacial interactions; iii) conformation of the polymer chains. These results raise many fundamental questions on the origin of the thickness-dependent glass transition. Why and how do the interactions with the substrate significantly affect T(g)( h)? Does T(g)( h) depend on the modifications of conformational parameters of the chains (their entropy)? What is the correlation between local dynamics and T(g)( h) in thin films? The aim of this paper is to summarise these open questions, which should stimulate further investigations in the thin polymer film scientific community.     

Self-organization of triblock copolymer patterns obtained by drying and dewetting

Self-organized block copolymer structures derived from dewetting of thin films are becoming important in nanotechnology because of the various spontaneous and regular sub-micrometric surface patterns that may be obtained. Here, we report on the self-organization of a poly(styrene)-b-poly(ethene-co-butene-1)-b-poly(styrene) triblock copolymer during drying of its solution over a mica substrate. Regular submicrometric arrangements with long-range order were formed at critical polymer concentrations, consisting of parallel ribbons and hexagonal arrays of dots (droplets). This variety of highly ordered structures is explained by the interplay between forming mechanisms, mainly due to “fingering instabilities” at the three-phase line of the copolymer solution during drying. The thickness of the structures was “quantized” due to the microphase separation of the block copolymer. The formation of hexagonal patterns may be attributed to Marangoni instability at the liquid film surface prior to dewetting.     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Stability of thin polymer films on a corrugated substrate

We study the wetting behaviour of thin polystyrene (PS) films on regularly corrugated silicon substrates. Below a critical film thickness the PS films are unstable and dewet the substrates. The dewetting process leads to the formation of nanoscopic PS channels filling the grooves of the corrugated substrates. Films thicker than the critical thickness appear stable and follow the underlying corrugation pattern. The critical thickness is found to scale with the radius of gyration of the unperturbed polymer chains. Received 6 April 2000 and Received in final form 24 August 2000     

Morphological instabilities of polymer crystals

We present experimental observations at comparatively low supercooling of morphology transitions from dendritic to faceted structures in polymer crystals growing in thin films of a poly-2-vinylpyridineblock-polyethyleneoxid copolymer. Our results are compared with theoretical concepts describing morphological instabilities of single crystals. Although these concepts originally were not developed for polymers, they allow to describe and interpret our experimental results quite well. In particular, the measured temperature dependence of the width W and frequency of dendritic side branches and the radius of curvature ρ of the growth tips of the crystals follow these concepts. We present preliminary evidence for the influence of polymer attachment kinetics and reorganisation processes behind the growth front. Polymer thin films provide valuable model systems for studying general concepts of crystallisation and allow to distinguish at which point the connectivity of the crystallising units within chain-like molecules starts to play a measurable role.     

Crystallization kinetics and crystal morphology in thin poly(ethylene oxide) films

We present a detailed study of the kinetics of crystallization for thin films of poly(ethylene oxide) (PEO). Measurements of the growth rate have been carried out using optical-microscopy techniques on films of monodisperse PEO. Films with thicknesses from 13 nm to ~2 m were crystallized isothermally at temperatures ~20°C below the melting point. A remarkable non-monotonic slowing-down of the crystal growth is observed for films with thickness less than ~400 nm. The changes in the growth rate from bulk-like values is significant and corresponds to a factor of 40 decrease for the thinnest films studied. The morphologies of isothermally crystallized samples are studied using atomic-force microscopy. We find that a morphology, similar to diffusion-controlled growth (dendritic growth and densely branched growth), is observed for films with h < 150 nm. In addition, changes in the morphology occur for thicknesses consistent with changes in the growth rate as a function of film thickness.     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

What can polymer crystal structure tell about polymer crystallization processes?

Contrary to most or all other materials, crystallization of chiral but racemic polymers such as isotactic polypropylene is accompanied by a conformational rearrangement which leads to helical geometries: the building units of the crystal are helical stems, -20nm long, which can be either right-handed or left-handed. Helical hand cannot be reversed within the crystal structure: it is therefore a permanent marker and an indicator of molecular processes (in particular segregation/selection of helical hands) which take place during crystal growth, and more precisely during the crucial step of “efficient” helical stem deposition. The issue of proper helical hand selection during polymer crystal growth is mainly illustrated with isotactic polypropylene. Its various crystalline polymorphs (, , and smectic) display virtually all possible combinations of helical hands, azimuthal settings and even non-parallel orientation of helix axes in space. Furthermore, a specific homoepitaxy which generates a lamellar branching in the phase “quadrites” and composite structures makes it possible a) to determine the helical hand and associated azimuthal setting of every stem in the crystalline entities and b) to determine the impact on the crystal structure and morphology of “mistakes” in helical hand of the depositing stem. Analysis of these morphologies demonstrates that the crystallization of isotactic polypropylene (and by implication of other achiral, helical polymers) is a highly sequential and “substrate-determined” process, i.e. that the depositing stem probes the topography of the growth face prior to attachment. These observations appear difficult to reconcile with crystallization schemes in which molecules (helical segments) are prearranged in a kind of pseudo-crystalline bundle (and as such, are not subjected to the high constraints of crystal symmetry) before deposition as a preassembled entity on the substrate. Received: 5 May 2000     

Heterogeneous dynamics at the glass transition in van der Waals liquids: Determination of the characteristic scale

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at T _g. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments. Received 29 March 2002 and Received in final form 11 November 2002 RID="a" ID="a"e-mail: long@lps.u-psud.fr     

The origins of fast segmental dynamics in 2 nm thin confined polymer films

Molecular-Dynamics computer simulations were used to study 2 nm wide polystyrene films confined in slit pores, defined by inorganic crystalline surfaces. The simulated systems mimic experimentally studied hybrid materials, where polystyrene is intercalated between mica-type, atomically smooth, crystalline layers. A comparison between the experimental findings and the simulation results aims at revealing the molecular origins of the macroscopically observed behavior, and thus provide insight about polymers in severe/nanoscopic confinements, as well as polymers in the immediate vicinity of solid surfaces. Pronounced dynamic inhomogeneities are found across the 2 nm thin film, with fast relaxing moieties located in low local density regions throughout the film. The origins of this behavior are traced to the confinement-induced density inhomogeneities, which are stabilized over extended time scales by the solid surfaces. Received 9 August 2001 and Received in final form 7 January 2002     

Partitioning of a heterotelechelic polystyrene to separate interfaces of thin films

Heterotelechelic deuteropolystyrenes have been synthesised with a tertiary amine functionality at one end and a fluorocarbon group at the other end of the polymer chain. A layer of this polymer, circa 120 ? thick, has been attached to the surface of a silicon substrate and subsequently covered with a much thicker layer of hydrogenous polystyrene. The combination has then been annealed at 413 K under vacuum for defined times and the subsequent distribution of the deutero heterotelechelic polymer determined using nuclear reaction analysis and neutron reflectometry. The influences of annealing time, molecular weight and thickness of the hydrogenous polymer have been examined. Nuclear reaction analysis showed that an excess of the heterotelechelic polymer formed at both interfaces with a larger excess remaining at the substrate-polymer interface. When the molecular weight of the hydrogenous polymer is lower than that of the deuteropolymer, the deutero layer is initially swollen by the hydrogenous polymer but the thickness then decreases as deutero polymer becomes detached from the silicon substrate and an additional excess layer is eventually formed at the vacuum-polymer surface. When the molecular weight of the hydrogenous polymer is higher, there is an initial shrinkage of the deuteropolymer layer, but the original thickness (∼ radius of gyration of the deuteropolymer) is regained on prolonged annealing. There is no evidence for bridging between the two interfaces by the heterotelechelic polymer. After five days annealing the volume fraction distribution of the deuteropolymer at the silicon substrate was well described by a self-consistent field model where the only adjustable parameter was the sticking energy of the tertiary amine group to the silicon substrate for which a value of 8k _B T was obtained. Comparison of the dependence of the equilibrium layer thickness of the deuteropolymer on the equilibrium grafting density at the silicon surface with the predictions of scaling theory for brush-like polymer layers suggested that the grafted molecules were in the ideal, unperturbed brush region. Received 12 October 2000 and Received in final form 27 March 2001     

Molecular dynamics in thin films of isotactic poly(methyl methacrylate)

The molecular dynamics in thin films (18 nm-137 nm) of isotactic poly(methyl methacrylate) (i-PMMA) of two molecular weights embedded between aluminium electrodes are measured by means of dielectric spectroscopy in the frequency range from 50 mHz to 10 MHz at temperatures between 273 K and 392 K. The observed dynamics is characterized by two relaxation processes: the dynamic glass transition (α-relaxation) and a (local) secondary β-relaxation. While the latter does not depend on the dimensions of the sample, the dynamic glass transition becomes faster (≤2 decades) with decreasing film thickness. This results in a shift of the glass transition temperature T _g to lower values compared to the bulk. With decreasing film thickness a broadening of the relaxation time distribution and a decrease of the dielectric strength is observed for the α-relaxation. This enables to deduce a model based on immobilized boundary layers and on a region displaying a dynamics faster than in the bulk. Additionally, T _g was determined by temperature-dependent ellipsometric measurements of the thickness of films prepared on silica. These measurements yield a gradual increase of T _g with decreasing film thickness. The findings concerning the different thickness dependences of T _g are explained by changes of the interaction between the polymer and the substrates. A quantitative analysis of the T _g shifts incorporates recently developed models to describe the glass transition in thin polymer films. Received 12 August 2001 and Received in final form 16 November 2001     

Acoustic instabilities in thin polymer films

The spatial confinement of a fluctuation spectrum leads to forces at the confining boundaries. While electromagnetic (EM) fluctuations lead to the well-known dispersion forces, the acoustic analogy has widely been neglected. We show that the strength of the forces resulting from confined acoustic modes may be of the same order of magnitude as van der Waals forces. Additionally, the predicted scaling behavior is identical to the non-retarded case of the EM fluctuations. Our results suggest that dewetting experiments using polymer films are strongly influenced by the acoustic dispersion forces. Received 5 March 2002 and Received in final form 21 May 2002     

Early stages of phase separation from polydisperse polymer mixtures

We study the early stages of phase separation in a mixture of a polydisperse and a monodisperse polymer within the Cahn-Hilliard framework. We model the polydisperse component using a finite, but arbitrarily large, number of components, and show that the number of components required for convergent behaviour to be achieved is computationally undemanding. We study the growth rate of fluctuations following a quench into the two-phase region of the phase diagram. The q-dependence of the growth rate is shown to be commensurate with the behaviour of a monodisperse-monodisperse mixture, with the major difference being an effective mobility that is dependent on the quench depth. We also study the deviation of the time dependence of the scattering function from single exponential behaviour. Received 29 June 2000 and Received in final form 20 November 2000     

Branched crystal morphology of linear polyethylene crystallized in a two-dimensional diffusion-controlled growth field

The branched crystal morphology of linear polyethylene formed at various temperatures from thin films has been studied by atomic-force microscopy (AFM), transmission electron microscopy (TEM), electron diffraction (ED) pattern and polymer decoration technique. Two types of branched patterns, i.e. dendrite and seaweed patterns, have been visualized. The fractal dimension d _f = 1.65 of both dendrite and some of seaweed patterns was obtained by using the box-counting method, although most of the seaweed patterns are compact. Selected-area ED patterns indicate that the fold stems tilt about 34.5^° around the b-axis and polymer decoration patterns show that the chain folding direction and regularity in two (200) regions are quite different from each other. Because of chain tilting, branched crystals show three striking features: 1) the lamella-like branches show two (200) regions with different thickness; 2) the crystals usually bend towards the thin region; 3) the thick region grows faster by developing branches, thus branches usually occur outside the thick region. The branched patterns show a characteristic width w, which gives a linear relationship with the crystallization temperature on a semilogarithmic plot. Received 15 March 2002 and Received in final form 29 April 2002